{"id":"palomar/PALOMAR-2026-08-21-000011","url":"https://github.com/lennrt/palomar-formalizations/tree/d259d35ad32d0e7c8c60ddd5a574aa987956e1d2/zenodo-21925458/palomar","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-21-000011-v2.json","repo":"https://github.com/lennrt/palomar-formalizations","tags":["math.CO","msc:05C12","msc:05C76","msc:68R10","graph-theory","metric-dimension","resolving-sets","lean-formalization"],"score":0,"title":"lennrt/palomar-formalizations","trust":"high","domain":"math.CO","source":"palomar","authors":["Lennart Rudolph"],"reviews":0,"subject":"math.CO","summary":"A concrete formalization of the infinite-family construction in the source: cycle and Cartesian-product distances on P_m □ C_(6m), the displayed landmarks (0,0), (0,2m), and (m-1,0), the four-piece cycle distance-pair locus, and injectivity of the resulting unordered multiset code for every even m at least 2. This establishes the three-landmark resolving upper bound. It does not formalize the separate general lower bound needed to conclude that the set is a basis or that the multiset dimension equals 3.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-03","reactions":{},"formalized":true,"formalizes":[{"title":"Multiset Dimension of Cylindrical Graphs: An Infinite Family and a Certified Census","identifier":"10.5281/zenodo.21925458","relationship":"formalizes"}]}